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In general liquidity is most often modeled, for most types of instruments, via proxy by the 'bid-ask spread'
(wider = less liquid, narrower = more liquid)

You can choose to model the bid-ask spread in dollars, or what is often most helpful, for options, is to model the bid-ask spread in terms of implied volatility (of the difference between the bid and ask prices). This lets you make consistent cross-sectional comparisons of liquidity, and do hypothesis testing.